Task control with remote center of motion constraint for minimally invasive robotic surgery

Minimally invasive surgery assisted by robots is characterized by the restriction of feasible motions of the manipulator link constrained to move through the entry port to the patient's body. In particular, the link is only allowed to translate along its axis and rotate about the entry point. This requires constraining the manipulator motion with respect to a point known as Remote Center of Motion (RCM). The achievement of any surgical task inside the patient's body must take into account this constraint. In this paper we provide a new, general characterization of the RCM constraint useful for task control in the minimally invasive robotic surgery context. To show the effectiveness of our formalization, we consider first a visual task for a manipulator with 6 degrees of freedom holding an endoscopic camera and derive the kinematic control law allowing to achieve the visual task while satisfying the RCM constraint. An example of application of the proposed kinematic modeling to a motion planning problem for a 9 degrees of freedom manipulator with assigned path for the surgical tool is then proposed to illustrate the generality of the approach.